|
Search: id:A163615
|
|
|
| A163615 |
|
a(n) = ((1+3*sqrt(2))*(4+sqrt(2))^n+(1-3*sqrt(2))*(4-sqrt(2))^n)/2. |
|
+0
4
|
|
| 1, 10, 66, 388, 2180, 12008, 65544, 356240, 1932304, 10471072, 56716320, 307135552, 1663055936, 9004549760, 48753614976, 263965223168, 1429171175680, 7737856281088, 41894453789184, 226825642378240, 1228082785977344
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Binomial transform of A163614. Fourth binomial transform of A163864. Inverse binomial transform of A163616.
|
|
FORMULA
|
a(n) = 8*a(n-1)-14*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
G.f.: (1+2*x)/(1-8*x+14*x^2).
|
|
PROGRAM
|
(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(4+r)^n+(1-3*r)*(4-r)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 06 2009]
|
|
CROSSREFS
|
Cf. A163614, A163864, A163616.
Sequence in context: A004310 A026853 A033504 this_sequence A117305 A108275 A086443
Adjacent sequences: A163612 A163613 A163614 this_sequence A163616 A163617 A163618
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
|
|
EXTENSIONS
|
Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 06 2009
|
|
|
Search completed in 0.002 seconds
|
